A Group Action on an R-Module and G-Module

Abstract

In this work, we introduce and study in the second part a new concept (the main result), which is called a group action on an module; in the third part, the group action on a ring  as -module; and in the fourth part, the relation between the -module and the group action on it. We give examples, properties, propositions, theorems, and corollaries about them.